Match List-I with List-II
| List-I | List-II | ||
| Differential Equation | Order and Degree | ||
| (A) | \( \left(y''\right)^{3}+5y'+3y=0 \) | (I) | 3, 4 |
| (B) | \( \left(y'''\right)^{2}+3\left(y''\right)^{3}+2y'+y=0 \) | (II) | 2, 2 |
| (C) | \( 2y''-\left[1+\left(y'\right)^{2}\right]^{3/2}=0 \) | (III) | 3, 2 |
| (D) | \( \left(y'''\right)^{4}+2\left(y''\right)^{2}+4y'+y=0 \) | (IV) | 2, 3 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) - (IV), (B) - (III), (C) - (II), (D) - (I)
The order is that of the highest derivative; the degree is the power of that derivative once the equation is free of radicals and fractional powers.
(A) The highest derivative is \( y'' \), to the power 3: order 2, degree 3. This matches (IV).
(B) The highest derivative is \( y''' \), to the power 2: order 3, degree 2. This matches (III).
(C) Squaring \( 2y''=\left[1+(y')^{2}\right]^{3/2} \) removes the fractional power:
\( \displaystyle 4(y'')^{2}=\left[1+(y')^{2}\right]^{3} \)
Order 2, degree 2. This matches (II).
(D) The highest derivative is \( y''' \), to the power 4: order 3, degree 4. This matches (I).
So the matching is (A) - (IV), (B) - (III), (C) - (II), (D) - (I).